Multi-Level Modeling of Oscillator Based Computation

Abstract

Emerging device technologies for nano-oscillators have inspired research in the use of oscillators to perform mathematical operations based on non-Boolean computations using the coupling behavior of an oscillator cluster, rather than CMOS logic gates. For example, circuits using coupled oscillators can be created to measure the Degree of Match (DOM) between two vectors. Coupled oscillators synchronize through a range of frequencies, called the locking region, depending on coupling strength. The output behavior of coupled oscillators with a DOM detector in the locking range has been shown to be the Euclidean distance squared, where larger DOM voltages correspond to more similar vectors. The convolution of two vectors can be calculated using three DOM oscillator clusters based on the algebraic expansion of Euclidean distance squared.Because the nano-oscillator devices have not matured enough to build large systems, it is important to design models of coupled oscillator behavior. Modeling oscillators is required across a hierarchy consisting of device models, circuit and logic models, and system models in order to support the entire scope of design abstractions. Device models are created by trial and error matching of the model to measured data. The system level model is then created by a polynomial fit to the output of a SPICE simulation of coupled oscillator circuits built using the circuit model. The result is a closed-form system level mathematical model usable in MATLAB and C++.This thesis presents a study of three models that span the discussed hierarchy: one STO model created based on two different circuit models with different detector characteristics, a VO2 oscillator model, and a generic parameterized model used to evaluate variations in oscillator parameters. All versions were tested at each level of the hierarchy and the results compared to control values to verify the models. The device level model was compared to the empirical data. The circuit level models were used to calculate DOM and convolution; these calculations were compared to MATLAB calculations. The system level models were tested in an image processing pipeline (IPP) and the accuracy of these models was compared to conventional floating-point calculations.